Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 8

Speedup: 1.0×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (+ z x))))

C

double code(double x, double y, double z) {
	return x + (y * (z + x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (z + x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (z + x));
}

Python

def code(x, y, z):
	return x + (y * (z + x))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z + x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (z + x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (+ z x))))

C

double code(double x, double y, double z) {
	return x + (y * (z + x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (z + x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (z + x));
}

Python

def code(x, y, z):
	return x + (y * (z + x))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(z + x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (z + x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x + z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y (+ x z) x))

C

double code(double x, double y, double z) {
	return fma(y, (x + z), x);
}

Julia

function code(x, y, z)
	return fma(y, Float64(x + z), x)
end

Wolfram

code[x_, y_, z_] := N[(y * N[(x + z), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot \left(z + x\right) + x} \]

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z + x, x\right)} \]

   3. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{x + z}, x\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x + z, x\right) \]
6. Add Preprocessing

Alternative 2: 61.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+33} \lor \neg \left(y \leq 1.9 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.15e+196)
   (* y z)
   (if (<= y -9.0)
     (* y x)
     (if (<= y 1.4e-88)
       x
       (if (<= y 1.22e-79)
         (* y z)
         (if (<= y 4.2e-34)
           x
           (if (or (<= y 1.35e+33) (not (<= y 1.9e+236)))
             (* y z)
             (* y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.15e+196) {
		tmp = y * z;
	} else if (y <= -9.0) {
		tmp = y * x;
	} else if (y <= 1.4e-88) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 4.2e-34) {
		tmp = x;
	} else if ((y <= 1.35e+33) || !(y <= 1.9e+236)) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.15d+196)) then
        tmp = y * z
    else if (y <= (-9.0d0)) then
        tmp = y * x
    else if (y <= 1.4d-88) then
        tmp = x
    else if (y <= 1.22d-79) then
        tmp = y * z
    else if (y <= 4.2d-34) then
        tmp = x
    else if ((y <= 1.35d+33) .or. (.not. (y <= 1.9d+236))) then
        tmp = y * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.15e+196) {
		tmp = y * z;
	} else if (y <= -9.0) {
		tmp = y * x;
	} else if (y <= 1.4e-88) {
		tmp = x;
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 4.2e-34) {
		tmp = x;
	} else if ((y <= 1.35e+33) || !(y <= 1.9e+236)) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.15e+196:
		tmp = y * z
	elif y <= -9.0:
		tmp = y * x
	elif y <= 1.4e-88:
		tmp = x
	elif y <= 1.22e-79:
		tmp = y * z
	elif y <= 4.2e-34:
		tmp = x
	elif (y <= 1.35e+33) or not (y <= 1.9e+236):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.15e+196)
		tmp = Float64(y * z);
	elseif (y <= -9.0)
		tmp = Float64(y * x);
	elseif (y <= 1.4e-88)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = Float64(y * z);
	elseif (y <= 4.2e-34)
		tmp = x;
	elseif ((y <= 1.35e+33) || !(y <= 1.9e+236))
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.15e+196)
		tmp = y * z;
	elseif (y <= -9.0)
		tmp = y * x;
	elseif (y <= 1.4e-88)
		tmp = x;
	elseif (y <= 1.22e-79)
		tmp = y * z;
	elseif (y <= 4.2e-34)
		tmp = x;
	elseif ((y <= 1.35e+33) || ~((y <= 1.9e+236)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.15e+196], N[(y * z), $MachinePrecision], If[LessEqual[y, -9.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.4e-88], x, If[LessEqual[y, 1.22e-79], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.2e-34], x, If[Or[LessEqual[y, 1.35e+33], N[Not[LessEqual[y, 1.9e+236]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.15000000000000001e196 or 1.39999999999999988e-88 < y < 1.22e-79 or 4.2000000000000002e-34 < y < 1.34999999999999996e33 or 1.89999999999999993e236 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.5%

      \[\leadsto x + \color{blue}{y \cdot z} \]

   4. Taylor expanded in z around inf 79.5%

      \[\leadsto \color{blue}{z \cdot \left(y + \frac{x}{z}\right)} \]

   5. Taylor expanded in z around inf 75.6%

      \[\leadsto \color{blue}{y \cdot z} \]

   if -3.15000000000000001e196 < y < -9 or 1.34999999999999996e33 < y < 1.89999999999999993e236

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(z + \frac{x}{y}\right)\right)} \]

   4. Taylor expanded in y around inf 99.0%

      \[\leadsto y \cdot \color{blue}{\left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.0%

         \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   6. Simplified 99.0%

      \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   7. Taylor expanded in z around 0 60.0%

      \[\leadsto \color{blue}{x \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 60.0%

         \[\leadsto \color{blue}{y \cdot x} \]

   9. Simplified 60.0%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -9 < y < 1.39999999999999988e-88 or 1.22e-79 < y < 4.2000000000000002e-34

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+33} \lor \neg \left(y \leq 1.9 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -4.8e-15)
     t_0
     (if (<= y 1.65e-88)
       x
       (if (<= y 6.5e-76) (* y z) (if (<= y 1.4e-34) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -4.8e-15) {
		tmp = t_0;
	} else if (y <= 1.65e-88) {
		tmp = x;
	} else if (y <= 6.5e-76) {
		tmp = y * z;
	} else if (y <= 1.4e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-4.8d-15)) then
        tmp = t_0
    else if (y <= 1.65d-88) then
        tmp = x
    else if (y <= 6.5d-76) then
        tmp = y * z
    else if (y <= 1.4d-34) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -4.8e-15) {
		tmp = t_0;
	} else if (y <= 1.65e-88) {
		tmp = x;
	} else if (y <= 6.5e-76) {
		tmp = y * z;
	} else if (y <= 1.4e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -4.8e-15:
		tmp = t_0
	elif y <= 1.65e-88:
		tmp = x
	elif y <= 6.5e-76:
		tmp = y * z
	elif y <= 1.4e-34:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -4.8e-15)
		tmp = t_0;
	elseif (y <= 1.65e-88)
		tmp = x;
	elseif (y <= 6.5e-76)
		tmp = Float64(y * z);
	elseif (y <= 1.4e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -4.8e-15)
		tmp = t_0;
	elseif (y <= 1.65e-88)
		tmp = x;
	elseif (y <= 6.5e-76)
		tmp = y * z;
	elseif (y <= 1.4e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-15], t$95$0, If[LessEqual[y, 1.65e-88], x, If[LessEqual[y, 6.5e-76], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.4e-34], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999999e-15 or 1.39999999999999998e-34 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(z + \frac{x}{y}\right)\right)} \]

   4. Taylor expanded in y around inf 96.3%

      \[\leadsto y \cdot \color{blue}{\left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 96.3%

         \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   6. Simplified 96.3%

      \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   if -4.7999999999999999e-15 < y < 1.64999999999999997e-88 or 6.5e-76 < y < 1.39999999999999998e-34

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.4%

      \[\leadsto \color{blue}{x} \]

   if 1.64999999999999997e-88 < y < 6.5e-76

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \color{blue}{y \cdot z} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(y + \frac{x}{z}\right)} \]

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{y \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -9.4e-7)
     t_0
     (if (<= y 9e-89)
       (+ x (* y x))
       (if (<= y 1.22e-79) (* y z) (if (<= y 4.8e-34) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -9.4e-7) {
		tmp = t_0;
	} else if (y <= 9e-89) {
		tmp = x + (y * x);
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 4.8e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-9.4d-7)) then
        tmp = t_0
    else if (y <= 9d-89) then
        tmp = x + (y * x)
    else if (y <= 1.22d-79) then
        tmp = y * z
    else if (y <= 4.8d-34) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -9.4e-7) {
		tmp = t_0;
	} else if (y <= 9e-89) {
		tmp = x + (y * x);
	} else if (y <= 1.22e-79) {
		tmp = y * z;
	} else if (y <= 4.8e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -9.4e-7:
		tmp = t_0
	elif y <= 9e-89:
		tmp = x + (y * x)
	elif y <= 1.22e-79:
		tmp = y * z
	elif y <= 4.8e-34:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -9.4e-7)
		tmp = t_0;
	elseif (y <= 9e-89)
		tmp = Float64(x + Float64(y * x));
	elseif (y <= 1.22e-79)
		tmp = Float64(y * z);
	elseif (y <= 4.8e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -9.4e-7)
		tmp = t_0;
	elseif (y <= 9e-89)
		tmp = x + (y * x);
	elseif (y <= 1.22e-79)
		tmp = y * z;
	elseif (y <= 4.8e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.4e-7], t$95$0, If[LessEqual[y, 9e-89], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-79], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.8e-34], x, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.4e-7 or 4.79999999999999982e-34 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(z + \frac{x}{y}\right)\right)} \]

   4. Taylor expanded in y around inf 97.0%

      \[\leadsto y \cdot \color{blue}{\left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 97.0%

         \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   6. Simplified 97.0%

      \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   if -9.4e-7 < y < 8.9999999999999998e-89

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.8%

      \[\leadsto x + \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative 3.5%

         \[\leadsto \color{blue}{y \cdot x} \]

   5. Simplified 77.8%

      \[\leadsto x + \color{blue}{y \cdot x} \]

   if 8.9999999999999998e-89 < y < 1.22e-79

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \color{blue}{y \cdot z} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(y + \frac{x}{z}\right)} \]

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{y \cdot z} \]

   if 1.22e-79 < y < 4.79999999999999982e-34

   1. Initial program 99.8%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -540.0) (not (<= y 0.0065))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.0065)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-540.0d0)) .or. (.not. (y <= 0.0065d0))) then
        tmp = y * (x + z)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.0065)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -540.0) or not (y <= 0.0065):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -540.0) || !(y <= 0.0065))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -540.0) || ~((y <= 0.0065)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -540.0], N[Not[LessEqual[y, 0.0065]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -540 or 0.0064999999999999997 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(z + \frac{x}{y}\right)\right)} \]

   4. Taylor expanded in y around inf 98.9%

      \[\leadsto y \cdot \color{blue}{\left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   6. Simplified 98.9%

      \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   if -540 < y < 0.0064999999999999997

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.0%

      \[\leadsto x + \color{blue}{y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.0) (not (<= y 0.0065))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.0) || !(y <= 0.0065)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.0d0)) .or. (.not. (y <= 0.0065d0))) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.0) || !(y <= 0.0065)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.0) or not (y <= 0.0065):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.0) || !(y <= 0.0065))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.0) || ~((y <= 0.0065)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.0], N[Not[LessEqual[y, 0.0065]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9 or 0.0064999999999999997 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(z + \frac{x}{y}\right)\right)} \]

   4. Taylor expanded in y around inf 98.9%

      \[\leadsto y \cdot \color{blue}{\left(x + z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   6. Simplified 98.9%

      \[\leadsto y \cdot \color{blue}{\left(z + x\right)} \]

   7. Taylor expanded in z around 0 53.4%

      \[\leadsto \color{blue}{x \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 53.4%

         \[\leadsto \color{blue}{y \cdot x} \]

   9. Simplified 53.4%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -9 < y < 0.0064999999999999997

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(x + z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y (+ x z))))

C

double code(double x, double y, double z) {
	return x + (y * (x + z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (x + z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * (x + z));
}

Python

def code(x, y, z):
	return x + (y * (x + z))

Julia

function code(x, y, z)
	return Float64(x + Float64(y * Float64(x + z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * (x + z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(x + z\right) \]
4. Add Preprocessing

Alternative 8: 36.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 38.0%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 38.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))